Rendiconti del Seminario Matematico della Università di Padova

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Volume 126, 2011, pp. 47–61
DOI: 10.4171/RSMUP/126-3

Published online: 2011-12-31

Quadratic Integral Solutions to Double Pell Equations

Francesco Veneziano[1]

(1) Scuola Normale Superiore, Pisa, Italy

We study the quadratic integral points--that is, ($S$-)integral points defined over any extension of degree two of the base field--on a curve defined in $\mathbb{P}_3$ by a system of two Pell equations. Such points belong to three families explicitly described, or belong to a finite set whose cardinality may be explicitly bounded in terms of the base field, the equations defining the curve and the set $S$. We exploit the peculiar geometry of the curve to adapt the proof of a theorem of Vojta, which in this case does not apply.

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Veneziano Francesco: Quadratic Integral Solutions to Double Pell Equations. Rend. Sem. Mat. Univ. Padova 126 (2011), 47-61. doi: 10.4171/RSMUP/126-3